Question: Simplify; express your answer in exponential form. Assume $k\neq 0, y\neq 0$. $\dfrac{{k^{5}y^{-1}}}{{(k^{-1}y)^{-4}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${k^{5}y^{-1} = k^{5}y^{-1}}$ On the left, we have ${k^{5}}$ to the exponent ${1}$ . Now ${5 \times 1 = 5}$ , so ${k^{5} = k^{5}}$ Apply the ideas above to simplify the equation. $\dfrac{{k^{5}y^{-1}}}{{(k^{-1}y)^{-4}}} = \dfrac{{k^{5}y^{-1}}}{{k^{4}y^{-4}}}$ Break up the equation by variable and simplify. $\dfrac{{k^{5}y^{-1}}}{{k^{4}y^{-4}}} = \dfrac{{k^{5}}}{{k^{4}}} \cdot \dfrac{{y^{-1}}}{{y^{-4}}} = k^{{5} - {4}} \cdot y^{{-1} - {(-4)}} = ky^{3}$